It has long been recognized that the accuracy of measurements of the bulk densities of earth formations adjacent a borehole by gamma-gamma logging is greatly affected by variations in the thickness of the mudcake formed on the wall of the borehole. Compensation for variations in mudcake thickness conventionally is obtained by using a sonde having two detectors located at different distances from the source and processing the count rate data from the two detectors by comparing them with data based on calibration of the sonde in natural or simulated formations of known densities with mudcakes of varying thicknesses and compositions.
The determination of corrected formation densities from count rate data from the sonde is based on a "spine and ribs" analysis of calibration data. FIG. 2 of the accompanying drawings shows a spine and ribs representation of calibration data from a generic two-detector sonde having a far-spaced detector and a near-spaced detector located 7 in. and 14 in. from the source, for example. Other locations are possible. The "spine" is formed by connecting the data points of the count rates of the detectors at different known formation densities with no mudcake. Each "rib" is obtained by connecting the near and far count rate data points for a single formation density and various thicknesses of a mudcake of the same density (1.2 g/cc. in the example of FIG. 2). Each data point is obtained with a uniform standoff between the sonde and the formation (uniform thickness mudcake).
The spine and ribs data can be converted into apparent density data that are functions of the count rates of the detectors and density correction data that are functions of the differences between the apparent densities determined from the count rates of the far and near detectors. The apparent density data and correction data are stored in a computer. In a logging run, the count rate data from the sonde are input to the computer and compared with the stored data to obtain a correction for mudcake density, which is added to the apparent density determined from the count rate of the far detector to obtain formation density. Reference may be made to Ellis, D. V., Well Logging for Earth Scientists, Elsevier Science Publishing Co., Inc., New York, 1987, for a detailed discussion of gamma-gamma density logging using two detector sondes.
For thin mudcakes, say up to 0.5 in., the spine and ribs correction for mudcake thickness is relatively insensitive to mudcake density. For thicker mudcakes, mudcake density introduces significant errors into the corrections. In the spine and ribs representation of FIG. 3, families of ribs for two formation densities and different mudcake thicknesses and densities are plotted. It is clear from FIG. 3 that different corrections to apparent densities computed from the far detector count rates are required for different mudcake densities. The problem is that the data from two detectors do not provide any way of taking into account differences in mudcake density in correcting the apparent density determined from the far detector count rate.